Chapter 4, Problem 83P

In Betty Crocker ‘s Cookbook, it is stated that it takes 2 h 45 mm to roast a 3.2-kg rib initially at 4.5°C to “rare” in an oven maintained at 163°C. It is recommended that a meat thermometer be used to monitor the cooking, and the rib is considered rare when the thermometer inserted into the center of the thickest part of the meat registers 60°C. The rib can be treated as a homogeneous spherical object with the properties $p=1200{\text{ kg/m}}^{\text{3}}\text{, cp = 4}\text{.1 kJ/kg}\text{.K, k = 0}\text{.45 W/m}\text{.K, }\alpha \text{ = 0}\text{.91 }\times {\text{ 10}}^{\text{-7}}{\text{ m}}^{\text{2}}\text{/s}$. Determine (a) the heat transfer coefficient at the surface of the rib: (b) the temperature of the outer surface of the rib when it is done: and (c) the amount of heat transferred to the rib. (d) Using the values obtained, predict how long it will take to roast this rib to “medium” level, which occurs when the If the roast rib is to be set on the counter for about 15 min before it is sliced, it is recommended that the rib be taken out of the oven when the thermometer registers about 4°C below the indicated value because the rib will continue cooking even after it is taken out of the oven. Do you agree with this recommendation? Solve this problem using the analytical one-term approximation method.